Consider a mass-spring system that oscillates with frequency w when there are no external forces acting on it. Now, suppose that the mass attached to the spring is initially 8 cm and then the mass is let go with an initial velocity of 4 cm/s. Furthermore, at time t = 9 s the mass is struck, once, with a hammer force of 7 grs cm/s^2.
Consider a mass-spring system that oscillates with frequency w when there are no external forces acting on it. Now, suppose that the mass attached to the spring is initially 8 cm and then the mass is let go with an initial velocity of 4 cm/s. Furthermore, at time t = 9 s the mass is struck, once, with a hammer force of 7 grs cm/s^2.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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![Consider a mass-spring system that oscillates with frequency w when there are no external forces acting on it. Now, suppose that the mass attached to
the spring is initially 8 cm and then the mass is let go with an initial velocity of 4 cm/s. Furthermore, at time t = 9 s the mass is struck, once, with a
hammer force of 7 grs cm/s^2.
The situation above can be described by the initial value problem
y" + w y = K 8(t – c),
y(0) = Yo,
y' (0) = Y1,
where, as usual, y(t) is the displacememnt of the spring from the equilibrium position in cm, positive downwards, at the time t in seconds, and the
hammer strike is modeled by a Dirac's delta generalized function.
Find the parameters K, c, yo and y1-
К —
Σ
c =
Σ
Yo =
Σ
Y1 =
Σ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57f71806-e3ea-4a27-9fc3-26b87b636dba%2F09d3c319-3b72-4f20-a52e-80dfbd2705be%2Fqykmbc_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a mass-spring system that oscillates with frequency w when there are no external forces acting on it. Now, suppose that the mass attached to
the spring is initially 8 cm and then the mass is let go with an initial velocity of 4 cm/s. Furthermore, at time t = 9 s the mass is struck, once, with a
hammer force of 7 grs cm/s^2.
The situation above can be described by the initial value problem
y" + w y = K 8(t – c),
y(0) = Yo,
y' (0) = Y1,
where, as usual, y(t) is the displacememnt of the spring from the equilibrium position in cm, positive downwards, at the time t in seconds, and the
hammer strike is modeled by a Dirac's delta generalized function.
Find the parameters K, c, yo and y1-
К —
Σ
c =
Σ
Yo =
Σ
Y1 =
Σ
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